From two frequency response measurements to the powerful nonlinear LFR model

Until now, in contrast to other block-oriented model structures, the nonlinear LFR model has received relatively little attention by the system identification and instrumentation and measurement communities. However, since it comprises a general multiple-input-multiple-output (MIMO) linear time-invariant part and a static nonlinearity (SNL), it allows one to represent any (complex) block-structure consisting of linear dynamic blocks and one SNL. This flexibility makes the LFR model an attractive candidate in real measurement applications. In this paper, a method is proposed for generating initial estimates of the nonlinear LFR model, starting from frequency response measurements carried out at 2 input amplitudes. In a first step, the MIMO linear dynamics are extracted from subspace representations of the linear models at both amplitudes, and in a second step, the SNL is identified from the input-output data, through the MIMO linear part. To support the theory, simulation examples are included, showing superior results compared to the linear models.